World Cup: increasingly random outcomes

The most striking feature of world soccer is that it has become far more egalitarian in terms of performance. The gap between good and bad teams has narrowed dramatically over time. An obvious measure of this is the average number of goals scored each game in the World Cup finals. Large differences in ability will be reflected in games in which teams are defeated by many goals.

The average was 3.89 in the first competition in 1930, rising to a record 5.38 in 1954. There was then a sharp fall to 2.78 in 1962, and ever since then it has fluctuated around 2.5, with the 2002 finals averaging 2.52 goals per game.

This is despite a big expansion in the number of teams in the final. At first there were only 13 teams, and from 1954 to 1978 just 16. The 1982-1990 competitions saw 24 teams, and in the last three there have been 32.

This trend to greater similarity of performance amongst teams is reflected in the qualifying rounds. In 1934, the first time there was a qualifying tournament to get into the finals, only 27 games were played. In 1990, there were 314 games, and for the 2006 finals no fewer than 847 games have already been played to decide which teams are in the finals.

The highest average goals per game was 5.22 in 1934 itself. After the Second World War there was a gradual fall to 2.74 in 1974, and it has since stayed around that level, with the 2006 qualifying rounds seeing an average of 2.91 goals per game.

Many matches are decided by a single goal, even between teams many places apart in the world rankings. This relatively narrow gap between teams implies a substantial element of randomness in success or failure. But perhaps this is part of the persistent appeal of an essentially trivial game which has few possibilities for innovation.